Optimal Scheduling Policies for Some Simple Transportation Systems

A transportation system is operated with one vehicle and several service points. Travel times between adjacent stops are random variables whose distribution functions are unchanged over a given period of time. The problem is to devise the scheduling strategy that minimizes average waiting time for passengers of the system. From the calculus of variations, and the principles advanced by Osuna and Newell for dealing with such problems, we are able to obtain a precise and simple statement of optimal policy for systems with one terminal stop at which interval control can be exerted. The special case of a two-stop line is analyzed in detail. An approximate optimal policy for systems with two terminals, very closely related to the one-terminal optimal strategy, is also suggested.